Abstract
The onset of Marangoni convection in an initially quiescent spherical droplet subjected to the impulsive change in boundary temperature is analyzed under the linear theory. For this system in which instabilities are driven by interface-tension gradients, a stability analysis on regular cell modes is conducted on the basis of the propagation theory we have developed. The present stability analysis predicts that τ c decreases with increasing Ma. For the limiting case of τ→0, the present study approaches the planar limit as expected.
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References
J. R. A. Pearson, J. Fluid Mech., 4, 489 (1958).
L. E. Scriven and C.V. Sternling, J. Fluid Mech., 19, 321 (1964).
J. C. Berg and A. Acrivos, Adv. Chem. Eng., 6, 61 (1966).
M. K. Smith and S. H. Davis, J. Fluid Mech., 132, 119 (1983).
O. Pirotte and G. Lebon, Appl. Microgravity Tech., 1, 175 (1988).
H. C. Hoefsloot and H.W. Hoogstraten, Appl. Microgravity Tech., 106, 2 (1989).
A. Cloot and G. Lebon, Microgravity Sci. Tech., 3, 44 (1990).
S. K. Wilson, J. Eng. Math., 28, 427 (1994).
A. Vidal and A. Acrivos, I&EC Fund., 7, 53 (1968).
K. H. Kang and C. K. Choi, Phys. Fluids, 9, 7 (1998).
K.H. Kang, I.G. Hwang and C.K. Choi, AIChE J., 46, 15 (2000).
R. J. Gumerman and G. M. Homsy, J. Fluid Mech., 68, 191 (1975).
K. K. Tan and R. B. Thorpe, Chem. Eng. Sci., 54, 775 (1999).
K. K. Tan, Int. J. Heat Mass Transfer., 48, 135 (2005).
V.M. Ha and C. L. Lai, Proc. R. Soc. London A, 457, 885 (2001).
J. F. Patzer and G. M. Homsy, Phys. Fluids, 24, 567 (1981).
V.M. Ha and C. L. Lai, Int. J. Heat Mass Transfer., 47, 3811 (2004).
M. C. Kim, J. H. Park and C. K. Choi, Chem. Eng. Sci., 60, 5363 (2005).
C.K. Choi, J.H. Park and M. C. Kim, Heat Mass Transfer., 41, 155 (2004).
M. C. Kim, J. S. Hong and C.K. Choi, AIChE J., 52, 2333 (2006).
M. C. Kim, C. K. Choi and J. K. Yeo, Phys. Fluids, 19, 084103 (2007).
M. C. Kim and C.K. Choi, Korean J. Chem. Eng., 26, 874 (2006).
M. C. Kim, T. J. Chung and C.K. Choi, Theoret. Comp. Fluid Dynamics, 18, 105 (2004).
M. C. Kim and C. K. Choi, Chem. Eng. Sci., 60, 599 (2005).
M.C. Kim, C. K. Choi, D.Y. Yoon and T. J. Chung, I&EC Res., 46, 5775 (2007).
H. S. Carslaw and J. C. Jaeger, Conduction of heat in solids, 2nd ed., Oxford Univ. Press, UK (1959).
J. Crank, The mathematics of diffusion, 2nd ed., Oxford Univ. Press, UK (1975).
J.-C. Chen, G. P. Neitzel and D. F. Jankowski, Phys. Fluids, 28, 749 (1985).
T. D. Foster, Phys. Fluids, 12, 2482 (1969).
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Kim, M.C., Yoon, DY. & Cho, E. Onset of marangoni convection in an initially quiescent spherical droplet subjected to the transient heat conduction. Korean J. Chem. Eng. 26, 1461–1466 (2009). https://doi.org/10.1007/s11814-009-0284-6
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DOI: https://doi.org/10.1007/s11814-009-0284-6